Appetizers and Lessons for Mathematics and Reason 
www.whyslopes.com        (missing links in the exposition of both)   ( Français)  
What does it mean to use a formula forwards and backwards

 Logic mastery is key to easing or avoiding learning difficulties in work & studies. 

Online Volumes (Book Orders)
1,  Elements of Reason. 1996
1A. Pattern Based Reason  1995
1B. Math Curriculum Notes 1996
2. Three Skills for Algebra  1995
3 .Why.Slopes.&
.More.Math.1995

Links To Tutoring Services

Parents:-Help. your. child. or. teen.study

Site  Math Folders

1. Arithmetic Flash Video Lessons  11-2008
2.  Algebra Videos (to appear)
3.-Fractions-Rates-Proportns-Units-2006
4.  Algebra, Odds & Ends, HS level-2001
5. 
Solving Linear Equations  04-2005
6.-Euclidean-Geometry/Complex No.s 
7.  Analytic Geometry/Functions 2006
8.  Number Theory. 2006-7
9.  Complex Numbers More 2001. 
 
10  Exponents, Radicals & logs. 2008
11. Calculus  2005

12.Real  Analysis 1995
13. Electric Circuits Etc  2007
Math Training
 How-TOs
/ Reference - 08- 2008
1. Arithmetic
2. Algebra 
3. More Algebra 
4. Geometry  
5. More Geometry
6. Calculus

Tutoring Services

[Tutorial Services][How Tutoring Services Differ] [Methods and Standards for Studies and Tutoring] [ Tutor Duties] [ Student Duties]

Tutorial Services

With some services, tutors are independent and you contact them directly. In other services, you ask for a tutor to be assigned.   Online, both students and tutor should be able to draw on the whiteboard and speak to each other.   See methods and standards below before you hire, and require them.  Good luck. 

In tutoring face to face and online, the quality of  help may vary greatly. For a tutor you do not know,  Arrange a first meeting and trial session free of charge.

Tutoring Services.

AU:  tutorfinder.com.au 
CDN :  findatutor.ca  
CDN: .i-tutor.ca  
CDN:  Montreal Tutors in Various Topics
NZ:   findatutor.co.nz  
UK:   tutorhunt.com  
UK:  tutors4me.co.uk  
USA: ziizoo.com
World:  TCYonline

The services provided here have not been evaluated. Use at your own risk. 

Reviewed Tutoring Services

For US students, TestCircle.com offers SAT and GMAT test preparation tutoring. It appears to be based on video streaming tutorials (flash) and includes excellent free samples - video lessons and practice test questions included.  I have not been online with their tutors. I am thinking of joining their affiliate program.   

 

How Tutoring Services Differ

  • Tutoring service may offer formal programs of study (short small-group courses)  with standard assignments and test, small to large, for their tutors and clients to follow. Diagnostic tests may determine skill level and hence program selection.  The programs or short-courses,  one at a time and one after another, provide more and more drill, practice and theory. The program requires the student to sit down and master the rules and conventions of mathematics, one at a time and one after  another.    
  • Tutors in contrast to tutoring services  may provide one lesson at a time, one lesson after another, without following a master plan, except to help a student catch up, keep up or stay ahead of a current course. This kind of service may  reflect the judgment of tutors and students. It can be more efficient if a tutor adjusts the pace and what is covered to reflect the needs and abilities of a student.  The best way to end coverage  is to halve the frequency of the lessons, but keep the tutor on board for periodic check-ups. 

Methods and Standards for Studies and Tutoring

As a parent, even before tutoring begins, you can insist your son or daughter keep and place in a binder their written work in mathematics to record their difficulties and progress.  Tell your son or daughter that neatness counts. Evaluation is based on what they write. There is more to mathematics than solving a question.  The work that led to the solution needs to be recorded to catch errors in reasoning - unwritten it is invisible - and to provide practice in presenting work clearly and fully. Any thing less is substandard.  Written work is the key.  There is more to mathematics than just obtaining a solution - presentation counts. While mathematics involves some mental agility,  writing and drawing on paper extends our memories and provide a tool for reasoning on paper and presenting the steps in their reasoning.   With practice, the number of steps and detail needed to show work may decrease but it should not disappear. 

Written Work: 
Insist that your son or daughter produce written work that records what is covered, the difficulties and the progress made.  Look at the neatness level of the work.   

The first meeting with a tutor is a time to say what you expect as the student, or parent of the student and to plan future sessions.  

For tutoring that supports course work,   identify the course and with the tutor form a list of skills and topics that need to be developed or checked.   Ask the tutor to say (a) which skills and concepts are needed for further studies, and to say (b) which are needed only for the next final examination.  Form a list of skills and topics to review, develop and check.   That may take more one meeting or session. Tutors should be paid for this planning time. 

Completeness: Students and their parents need to identify the skills and topics they want to master, and say they are willing to provide the time to meet and master any earlier skills and topics that are required. The rules and conventions at each level of mathematics need to be mastered fully and completely.   While there may be more rules and conventions than a student may  want to learn and follow, the key ones cannot be skipped. Think of the young child who insists there are too many letters in the alphabet to learn.  We know better. All the letters need to be recognized for the sake of spelling, reading and writing. Likewise in mathematics,  key skills and concepts cannot be skipped. 

Checks are very important. In face to face tutoring and education, tutors and teachers can collect and place in a binder, the written work of a student to record progress and/or difficulty.  The emphasis on written work - doing mathematics on paper clearly and properly - is necessary since students performance in mathematics is mostly based on it. In online tutoring,  students should turn their written work into pdf or image files with the aid of electronic scanners, and then email that work to the tutor for correction.   Two way faxing or regular mail provide alternatives.  

Parents - Do not Blame your son or daughter for all difficulties in mathematics: The site author has meet incoherent, indecipherable textbooks approved and required for use in school classroom by bureaucrats.  If you cannot understand a textbook, ask fellow parents or people with a good background in mathematics if they can.  Sometimes the fault in education is not with your child or teen, it is with the textbooks and training of their teachers. Many schools employ teachers untrained in mathematics to give mathematics courses. So their habits may be self-formed. Combine that with subtandard textbooks and your school district is providing substandard training in mathematics.   

For a program studies planned by the tutor and student,  tutorial sessions may (i) correct written work in front of the student(s),  (ii) cover more material, and (iii) arrange for more written work to be submitted - an assignment from the tutor and/or a selection of the written work the student has to do or has done for a course.  Good luck.

Tutor Duties

  • Explain skills and concepts
  • Use proper notation in explanations to provide a model for students to follow.
  • Correct answers and more importantly, the written work that led to those answers.
  • Arrange and test methods for the submission of written work, and 
    the correction of the latter in front of the student
  • Plan or follow program of studies with a student (recommended) OR
     help the student on demand without looking ahead. 
  • Tell students when they are skipping skills and concepts that need to be mastered.
  • Ethics I: Withdraw your services when a student insists on trying to cover material for which they are not prepared.  

Student Duties

  • Be willing to review earlier skills and topics as needed? Students who insist on skipping earlier skills and topics needed for later ones are inviting trouble.  
  • If you can,  identify where your skills need help or where you need to check your work. Providing a course description could be enough to identify and locate what ideas you want to cover. Try to make a long term plan of studies and with your tutor try to understand in what needs to be done earlier and what will be done later. 

    Gifted students may consult a tutor for help with details or nuances. 
  • Prepare in advance if possible, so that the tutor spends more and more time explaining errors what you have done and less time watching you work. The written may stem from questions that a tutor sets. 

    Arrange and test methods for the submission of written work, and the correction of the latter in front of the student. For online tutoring scan your written work into say pdf format, and then (a) email the pdt file(s) to your tutor, or (b) upload them during the tutoring session. The www.WiZIQ.com site provides a platform for this (membership is free). It may be ad-supported. 

  • Watch the written work of your tutor, your fellow students and teacher for proper ways to present and format your own work.  
  • Compare and contrast the work and presentation of your tutor and teachers with that in course textbooks.   Course textbooks often set a standard to follow for the presentation of written work. Look at the location of equal signs, arithmetic signs for addition, subtraction, multiplication and roots. Look at how fractions and mixed numbers are written. 
  • Getting Help With Problems.  Students should ask fellow students, parents and tutors for help in understanding how to solve problems and in checking or correcting their written work for all errors of logic and presentation.  That extra effort and training may lead to better marks for the homework,  but more importantly, it may lead to better skills and comprehension.  The better marks can be seen as a reward for seeking the help and correction before submitting work for marks.  In the foregoing, students may copy, but students who have to copy will be caught on tests and final examinations.   So if you are a student getting help,  you should use it to improve your own skills and knowledge, and not just to copy - the latter would be a waste of time, and in the case of tutoring, the money paid for it. 

 

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